I presume they wouldn't move to a smaller house if you weren't there, so charging you for the physical space doesn't make sense to me.

Sometimes it's not about the *cost* as much as it's about the *worth*. It might not cost anything to have someone live with you, beyond a few bucks in increased utilities, but the worth is determined by the parties involved.

A spare bedroom in my house, with food for one, might cost $200.

It would take much, much more than that for me to let someone move in that room. The privacy would be worth a lot more than the cost of $200.

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